You can mate in two if the computer goofs: Qf4, which both times I’ve done it against the computer it baited them into Rxg2, and then Qxh6 is mate. Obviously it is slightly different if, say, the computer, instead of Rxg2, it did Rg6. This puts a halt on the mate in two, and in the strategy in general. I haven’t worked completely through the solution, but i have a hunch it is a sure fire way to get a mate.